Finally, a “standard" constraint on multiscalar models is to verify their compliance with electroweak precision bounds i.e. constraints on the oblique \(S,T\)  and \(U\)  parameters. Models with \(N\)  Higgs doublets automatically satisfy \(\rho = 1\)  at tree-level, which means that bounds on the oblique parameter \(S\)  will be easily satisfied. However, that is no longer true for the \(T\)  parameter, which typically needs to be computed for any given model. Constraints on \(T\)  typically enforce, for very high masses, degeneracies between the extra scalars in the mass spectrum of the model. The results from Ref. [1]} are of no help to us in this case, as the expressions for the oblique
parameters given there are only valid for a 3HDM version of the inert type (where one of the doublets is
VEVless and naturally decouples from the gauge sector).
